ps07 - Physics 651 – Problem Set 7(due Read Chapter 3 to...

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Unformatted text preview: Physics 651 – Problem Set 7 (due 10/27/03) Read Chapter 3 to p. 63. You may choose to spend a minimal amount of time on the wrong canonical (commutator) quantization of the Dirac field. 1. Using Eq.(3.99), (3.101) and other properties of the Dirac spinor, derive Eq.(3.102) and (3.104). 2. Derive the Noether current associated with the invariance of the Dirac action under the phase redefinition ψ ( x ) → e iα ψ ( x ). Show that the corresponding conserved charge is Q = R d 3 x ψ † ( x ) ψ ( x ), and express this charge in terms of creation and annihilation operators. (You may drop an infinite constant as usual.) Evaluate the charges of 1-particle electron and positron states. 3. For a massless Dirac field, derive the Noether current associated with the invariance of the Dirac action under the phase redefinition ψ ( x ) → e iαγ 5 ψ ( x ). This is the axial-vector current. Show that the left-handed current j μ L given in Eq.(3.76) is a function only of left- handed field...
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ps07 - Physics 651 – Problem Set 7(due Read Chapter 3 to...

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